The number of proper divisors of the number o | vedclass

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(B) First,we find the prime factorization of $13!$: $13! = 2^{10} 	imes 3^5 	imes 5^2 	imes 7^1 	imes 11^1 	imes 13^1$. Dividing $13!$ by $100$ (

Vedclass · Accepted Answer

$430$

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(B) First,we find the prime factorization of $13!$: $13! = 2^{10} 	imes 3^5 	imes 5^2 	imes 7^1 	imes 11^1 	imes 13^1$. Dividing $13!$ by $100$ (which is $2^2 	imes 5^2$): $\frac{13!}{100} = \frac{2^{10} 	imes 3^5 	imes 5^2 	imes 7^1 	imes 11^1 	imes 13^1}{2^2 	imes 5^2} = 2^8 	imes 3^5 	imes 7^1 	imes 11^1 	imes 13^1$. The total number of divisors is given by $(8+1)(5+1)(1+1)(1+1)(1+1) = 9 	imes 6 	imes 2 	imes 2 	imes 2 = 432$. The number of proper divisors is the total number of divisors excluding the number itself and $1$,so we subtract $2$: $432 - 2 = 430$.

The number of proper divisors of the number obtained by dividing $13!$ by $100$ is

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